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Stability of Geothermal Convection in Anisotropic River Beds

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Document pages: 23 pages

Abstract: The onset of thermal convection, due to heating frombelow in a system consisting of a fluid layer overlying a porous layer withanisotropic permeability and thermal diffusivity, is investigated analytically.The porous medium is both anisotropic in permeability whose principal axes areoriented in a direction that is oblique to the gravity vector and in thermal conductivitywith principal directions coincident with the coordinate axes. The Beavers-Josephcondition is applied at the interface between the two layers. Based on parallelflow approximation theory, a linear stability analysis is conducted to studythe geothermal river beds system and documented the effects of the physicalparameters describing the problem. The critical Rayleigh numbers for both thefluid and porous layers corresponding, to the onset of convection arising fromsudden heating and cooling at the boundaries are also predicted. The results obtainedare in agreement with those found in the past for particular isotropic andanisotropic cases and for limiting cases concerning pure porous media and forpure fluid layer. It has demonstrated that the effects of anisotropicparameters are highly significant.

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